Unlock the star cup and play it.
You unlock her in either a 50cc race or a 100cc race in Special Cup.
Win first place in 50cc,100cc or 150cc special cup
you have to beat 50cc
50cc star cup
In order to unlock this kart, you must win the 50CC Leaf Cup.
Do 50cc and get at least one star rank in all 50cc cups
Win the 50cc Star Cup.
Complete the other three cups on 100cc. You do the same for 150cc as well. Note that you can't unlock the Special Cup for 50cc, since it isn't available for that difficulty.
all star on 50cc
win the 50cc lightning cup to unlock diddy kong
If you need to unlock her in Mario kart wii here is the answer: Win the 150cc Special Cup. If you need to unlock her in Mario Kart 7 here is the answer: Win the 150cc Mushroom Cup. Source: I beat Mario Kart Wii, and I unlock Daisy in Mario Kart 7.
In Mario kart wii you have to win the 150cc special cup